Numerical technique for solving generalized integro- differential-difference equation with variable coefficient combined ultraspherical-Galerkin method
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Date
2026-02
Journal Title
Journal ISSN
Volume Title
Publisher
Arid Zone Journal of Basic and Applied Research Faculty of Science, Kashim Ibrahim University Maiduguri, Nigeria
Abstract
This study proposes a numerical technique for obtaining approximate
solutions to generalized integro-differential-difference equations with variable
coefficients using the Ultraspherical–Galerkin method. The method
transforms the original equation into a system of algebraic equations. The
approximate solution is expressed in terms of shifted ultraspherical
polynomials. The stability and convergence of the proposed technique are
analyzed. The accuracy and effectiveness of the method are further validated
through several benchmark problems selected from the literature